Simplify √n

Steps

1. Find the largest square factor of n: 4, 9, 16, 25, 36, 49, …
2. √n = √(square × rest) = √square × √rest.
3. Check that the number left under the root has no square factor: √72 = √(36 × 2) = 6√2, and 2 has none.

Worked examples

= √(4×3) + √(9×3)
= 2√3 + 3√3
= 5√3

For the whole topic, read Surds: key points, common mistakes and how the DSE tests it.

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